Here are the solutions to your Math Puzzles MCQs.

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• If, R=(xT-4) when, T=5, R=16. Then find the value of R when, T=8

          Ans:           R = xT-4

                       or, 16 = 5x-4

                       or,  5x = 20

                       or,  x = 4 ........(i)

              again,   R = xT-4

                      or,   R = 4*8-4 [ I get it from (i) ]

                      or,   R = 32-4 

                      or,   R = 28 

• If, x = (1-2q), y = (2q+5), q = ? [x = y] 

      Ans:       as,  x = y

                  then,  1-2q = 2q+5

                       or,   4q = (-4)

                       or,    q = (-1) 

• If, p/4=q/5=r/9, then find the value of (p+q+r)/r.

   Ans:             p/4 = q/5 = r/9 = k (k>0)

                so,    p = 4k,   q = 5k,   r = 9k

           now, (p+q+r)/r = (4k+5k+9k)/9

                or,  (p+q+r)/r   =  18k/9k

                     or,  (p+q+r)/r  =  2 

• If, y = (x+4)^2, then find the value of {(-3x)-12}^2 ?

    Ans:     y = x^2+2*x*4+4^2

            or,   9*y = 9*(x^2+2*x*4+4^2)

            or,    9y =  9x^2+72x+144......(i)

           now,  {(-3x)-12}^2

                  =  9x^2+72x+144

                  =  9y  [ I get it from (i) ] 

• If, x+3y=8 and xy=6, then find the value of 9/x+3/y.

     Ans:      x+3y=8 
                or, 3y = 8-x

                or, 9y = 24-3x.....(i)

               9/x + 3/y = (9y+3x)/xy
              or,  9/x + 3/y = (24-3x+3x)/6  [ I get it from (i) ]

              or,  9/x + 3/y = 24/6
              or,  9/x + 3/y = 4  

• If, 2^p+3^q=25 and 2^(p+2)-3^(q+1)=37, then find the value of p and q.

 Ans:            { 2^(p+2) – 3^(q+1) } = 37
               or,  { (2^p × 4) – (3^q × 3) } = 37
             or,  (4x – 3y)  =  37 [ Let’s say that, 2^p = x and 3^q = y ]

 

now,   x + y = 25…..(i) × 4

          4x – 3y = 37….(ii) × 1

 

now,   4x + 4y = 100…..(i)

           4x – 3y = 37…….(ii)

___(-)___(+)___(-)_________

                7y  =  63
           or,  y  =  9

now, x = 25 – 9 = 16

Now,      2^p = 16                  |                 3^q = 9

          or,  2^p = 2⁴                    |                or,  3^q = 3²

              or,   p = 4              |          or,   q = 2 

   

•  If, x/(y+z)=y/(z+x)=z/(x+y)=k (x+y+z not is equal to 0), then determine the value of k.

    Ans:     now,  x = k(y+z)
                          y = k(z+x)
                          z = k(x+y)

        now,     x+y+z = ky + kz + kz + kx + kx + ky
                  or,  x+y+z = 2kx + 2ky + 2kz
                  or,  x+y+z = 2k(x+y+z)
                   or,    2k   =   1
                    or,   k = 1/2 

 # The number 571 is considered a prime number because it satisfies the definition of a   prime number. It is a natural number greater than 1 that has exactly two distinct positive   divisors, which are 1 and itself.

# The numbers that remain after the elimination process are the prime numbers less than 70. These are:  2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67.

  

                           (y+a)(y-b)

      Ans:     =   y²  - by + ay - ab
                  =   y² - y (b - a) - ab
                =   y² - y {- (a - b) } – ab
                  =   y² + y (a - b) - ab